5x=2x^2-x+9

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Solution for 5x=2x^2-x+9 equation:


Simplifying
5x = 2x2 + -1x + 9

Reorder the terms:
5x = 9 + -1x + 2x2

Solving
5x = 9 + -1x + 2x2

Solving for variable 'x'.

Reorder the terms:
-9 + 5x + x + -2x2 = 9 + -1x + 2x2 + -9 + x + -2x2

Combine like terms: 5x + x = 6x
-9 + 6x + -2x2 = 9 + -1x + 2x2 + -9 + x + -2x2

Reorder the terms:
-9 + 6x + -2x2 = 9 + -9 + -1x + x + 2x2 + -2x2

Combine like terms: 9 + -9 = 0
-9 + 6x + -2x2 = 0 + -1x + x + 2x2 + -2x2
-9 + 6x + -2x2 = -1x + x + 2x2 + -2x2

Combine like terms: -1x + x = 0
-9 + 6x + -2x2 = 0 + 2x2 + -2x2
-9 + 6x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-9 + 6x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
4.5 + -3x + x2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + -3x + -4.5 + x2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + -3x + x2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + -3x + x2 = 0 + -4.5
-3x + x2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
-3x + x2 = -4.5

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -4.5 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -4.5 + 2.25

Combine like terms: -4.5 + 2.25 = -2.25
2.25 + -3x + x2 = -2.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = -2.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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